Four-wheel steering vehicles are provided with steerable rear wheels, and the rear wheels are normally steered so as to provided an optimum lateral response of the vehicle according to the traveling speed of the vehicle, and the steering angle of the front wheels. For instance, a target yaw rate is defined according to the operating condition of the vehicle, and the rear wheels are steered so as to achieve the target yaw rate. However, this target yaw rate is defined for a normal tire and for a fixed predetermined road condition, and may not necessarily give rise to an optimum lateral response of the vehicle depending on the conditions of the tires and the road surface. In particular, it is desirable to know the road friction or the friction between the tires and the road surface because the optimum lateral response of the vehicle depends much on the road friction. For instance, the properties of the tires (snow tires and high performance tires as opposed to normal tires), the weather conditions (snow accumulation, moisture on the road surface) and other conditions of the road surface can significantly change the road friction.
It is possible to estimate the road friction according to the internal pressure of the hydraulic cylinder of the power steering system. A number of sophisticated methods have been proposed in the past, but they are either too expensive or too unreliable to implement.
It is conceivable to indirectly estimate the road friction from the operating conditions of the vehicle, the lateral response of the vehicle, and an output from a yaw rate sensor. However, the lateral response of the vehicle can be accurately expressed only by a transfer function of at least second order if it can be expressed with a linear function with a sufficient accuracy at all. It is known that the lateral response depends significantly on the vehicle speed. Thus, the algorithm for identifying the transfer function for the lateral response tends to be highly complex so that the capacity of the ECU (electronic control unit) for the four-wheel steering control needs to be unduly great. Thus, according to this approach, a high cost is required, and, yet, it is doubtful if a desired accuracy can be attained.